s算术齐次空间中的多项式动态轨道和点阵轨道

Q4 Mathematics

Confluentes Mathematici Pub Date : 2009-02-11 DOI:10.1142/S1793744210000120

A. Guilloux

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引用次数: 5

摘要

考虑一个局部紧群G下的齐次空间和G中的一个格Γ，那么这个格自然作用于齐次空间。看着一个密集的轨道，人们可能想知道如何描述它的重划分。然后采用动力学的观点，将轨道上点的渐近分布与空间上的自然测度进行比较。在李群及其齐次空间的背景下，一些结果表明轨道上的点是均匀分布的。我们在p进和s算术群的集合中讨论这个问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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POLYNOMIAL DYNAMIC AND LATTICE ORBITS IN S-ARITHMETIC HOMOGENEOUS SPACES

Consider a homogeneous space under a locally compact group G and a lattice Γ in G. Then the lattice naturally acts on the homogeneous space. Looking at a dense orbit, one may wonder how to describe its repartition. One then adopts a dynamical point of view and compare the asymptotic distribution of points in the orbits with the natural measure on the space. In the setting of Lie groups and their homogeneous spaces, several results show an equidistribution of points in the orbits. We address here this problem in the setting of p-adic and S-arithmetic groups.

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来源期刊

Confluentes Mathematici Mathematics-Mathematics (miscellaneous)

CiteScore

0.60

自引率

0.00%

发文量

期刊介绍： Confluentes Mathematici is a mathematical research journal. Since its creation in 2009 by the Institut Camille Jordan UMR 5208 and the Unité de Mathématiques Pures et Appliquées UMR 5669 of the Université de Lyon, it reflects the wish of the mathematical community of Lyon—Saint-Étienne to participate in the new forms of scientific edittion. The journal is electronic only, fully open acces and without author charges. The journal aims to publish high quality mathematical research articles in English, French or German. All domains of Mathematics (pure and applied) and Mathematical Physics will be considered, as well as the History of Mathematics. Confluentes Mathematici also publishes survey articles. Authors are asked to pay particular attention to the expository style of their article, in order to be understood by all the communities concerned.